Thanks for the suggestions guys...

A long time on the phone to both BA rebooking centre and the Exec Club, all of whom tell me that Bermuda is the best way out (I don't think the system comprehends any solution that involves driving between airports rather than sitting in Bermuda for 7 hours).

I've kinda timed out and had to check in to the United Flight. Hopefully I'll get out of the airport at some stage.

Y all the way I'm afraid. Best thing to do is to grin and bear it.